Evaluating the sensitivity of jurisdictional heterogeneity and jurisdictional mixing in national level HIV prevention analyses: context of the U.S. ending the HIV epidemic plan

Background The U.S. Ending the HIV epidemic (EHE) plan aims to reduce annual HIV incidence by 90% by 2030, by first focusing interventions on 57 regions (EHE jurisdictions) that contributed to more than 50% of annual HIV diagnoses. Mathematical models that project HIV incidence evaluate the impact of interventions and inform intervention decisions. However, current models are either national level, which do not consider jurisdictional heterogeneity, or independent jurisdiction-specific, which do not consider cross jurisdictional interactions. Data suggests that a significant proportion of persons have sexual partnerships outside their own jurisdiction. However, the sensitivity of these jurisdictional interactions on model outcomes and intervention decisions hasn’t been studied. Methods We developed an ordinary differential equations based compartmental model to generate national-level projections of HIV in the U.S., through dynamic simulations of 96 epidemiological sub-models representing 54 EHE and 42 non-EHE jurisdictions. A Bernoulli equation modeled HIV-transmissions using a mixing matrix to simulate sexual partnerships within and outside jurisdictions. To evaluate sensitivity of jurisdictional interactions on model outputs, we analyzed 16 scenarios, combinations of a) proportion of sexual partnerships mixing outside jurisdiction: no-mixing, low-level-mixing-within-state, high-level-mixing-within-state, or high-level-mixing-within-and-outside-state; b) jurisdictional heterogeneity in care and demographics: homogenous or heterogeneous; and c) intervention assumptions for 2019–2030: baseline or EHE-plan (diagnose, treat, and prevent). Results Change in incidence in mixing compared to no-mixing scenarios varied by EHE and non-EHE jurisdictions and aggregation-level. When assuming jurisdictional heterogeneity and baseline-intervention, the change in aggregated incidence ranged from − 2 to 0% for EHE and 5 to 21% for non-EHE, but within each jurisdiction it ranged from − 31 to 46% for EHE and − 18 to 109% for non-EHE. Thus, incidence estimates were sensitive to jurisdictional mixing more at the jurisdictional level. As a result, jurisdiction-specific HIV-testing intervals inferred from the model to achieve the EHE-plan were also sensitive, e.g., when no-mixing scenarios suggested testing every 1 year (or 3 years), the three mixing-levels suggested testing every 0.8 to 1.2 years, 0.6 to 1.5 years, and 0.6 to 1.5 years, respectively (or 2.6 to 3.5 years, 2 to 4.8 years, and 2.2 to 4.1 years, respectively). Similar patterns were observed when assuming jurisdictional homogeneity, however, change in incidence in mixing compared to no-mixing scenarios were high even in aggregated incidence. Conclusions Accounting jurisdictional mixing and heterogeneity could improve model-based analyses. Supplementary Information The online version contains supplementary material available at 10.1186/s12874-022-01756-w.


A3: Estimation of incidence using Bernoulli
85 § Numbers within parenthesis "()" refer to compartment numbers as seen in Figure 1.

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We estimate the number of persons transitioning from the susceptible to infected compartments, i.e., the number of

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We calculate the number of new infections in risk group * and age group * as (2)

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)*,,* is the number of susceptible individuals in risk group * , and age group * ; 119 1 − M 0 ! ,1 ! ,2 is the transmission probability per partnership for a susceptible person in risk group * and age group * 120 from interactions with an infected person in compartment , and is calculated as ,

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Data related to the above parameters are presented in Tables A5 to A14.

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The total number of new infections in the National-Model for all risk groups and age groups, can then be calculated 148 as follows: We estimate the number of new infections as in (2) but now also include jurisdictional mixing of sexual partnerships 155 as follows.

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Number of new infections in risk group * , age group * , and jurisdiction = 158        Table A9: Proportion of condom usage * by risk group, partnership type and age group [28,29] 189

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A4: Estimation of diagnosis and retention-in-care rates 213 As care parameters change over time, the diagnosis and retention in care rates also change. Therefore, we 214 analytically estimate these in the model, by calibrating it to the expected targets for the care continuum metrics, 215 specifically, the % aware, and % VLS. We calculate diagnosis rate and retention-in-care rate specific to risk group 216 and jurisdiction only (and not specific to age or disease stage), and thus use a collapsed/simplified state of the 217 Markov process (Eqn. 1 in Section A1) as follows (see Figure A1).

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We estimate rates ! and ! by expansion of the above equations as discussed in following sub-sections. We estimate 240 these rates specific to risk group for the National-Model and specific to both risk group and jurisdiction for the 241 Jurisdictional-Model but exclude the jurisdictional notation for clarity.

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Each term on the right-hand-side of (10) is computationally calculated in the simulation as follows:

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We are only estimating the dropout rate for CD4 count >200. For CD4 count <200, we assume dropout is 0 and this 287 is modeled by making " = 0 for CD4 count < 200.

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Expanding (8)   infection/AIDS so we assume they will stay in care) for each risk group ,

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Each term in the right-hand-side of (12) is computationally calculated in the simulation as follows:

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• !9* !9*,P,$%&' is the number of people in compartment at previous time-step and is tracked in the

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Then we can write,